Nonhomogeneous fractional integration and multifractional processes
Extending the recent work of Philippe et al. [A. Philippe, D. Surgailis, M.-C. Viano, Invariance principle for a class of non stationary processes with long memory, C. R. Acad. Sci. Paris, Ser. 1. 342 (2006) 269-274; A. Philippe, D. Surgailis, M.-C. Viano, Time varying fractionally integrated processes with nonstationary long memory, Theory Probab. Appl. (2007) (in press)] on time-varying fractionally integrated operators and processes with discrete argument, we introduce nonhomogeneous generalizations I[alpha]([dot operator]) and D[alpha]([dot operator]) of the Liouville fractional integral and derivative operators, respectively, where , is a general function taking values in (0,1) and satisfying some regularity conditions. The proof of D[alpha]([dot operator])I[alpha]([dot operator])f=f relies on a surprising integral identity. We also discuss properties of multifractional generalizations of fractional Brownian motion defined as white noise integrals and s.
Year of publication: |
2008
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Authors: | Surgailis, Donatas |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 118.2008, 2, p. 171-198
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Publisher: |
Elsevier |
Keywords: | Liouville fractional operators Long-range dependence Multifractional Brownian motion Nonhomogeneous fractional integration Scaling limits |
Saved in:
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